In addition to its biological plausibility, our SNN model is capable of learning sequences of binary vectors, or spatiotemporal patterns of spikes. In the deterministic limit, this network, a McCulloch-Pitts network [1]}, is a generalization of the Hopfield network that allows asymmetric connections between fully-visible binary units.
As a result, deterministic dynamics in the state space can converge to an attractor of period larger than one (a cycle), as opposed to a fixed-point corresponding to a static spatial memory in the Hopfield network.
We demonstrate that the network can be trained to memorize repeating sequences of binary vectors and that the spatiotemporal memory is robust to perturbation. In particular, given an arbitrary initial state of the spike pattern, the dynamics generated by the trained network converge to a memorized cycle.
Thus, the STDP-consistent McCulloch-Pitts network performs a spatiotemporal pattern completion, generalizing the classical Hopfield network that performs spatial pattern completion.
In the noisy limit, the trained network can be regarded as a generative model for spatiotemporal patterns of spikes that performs sampling of both the time to the next spiking event and the neuron to next spike.
We illustrate that this network efficiently performs inference on continuous-time data from a neurobiology experiment, and we discuss its applicability to inference problems in neuroscience.
